To move the hand from one point to another, the brain controls the arm's movement by relying on neural structures that estimate physical dynamics of the task and transform the desired motion into motor commands. If the hand is holding an object or otherwise interacting physically with the environment, the resulting changes in arm dynamics are taken into account by these structures, resulting in altered motor commands. This suggests that in generating motor commands, the brain relies on internal models that predict the physical dynamics of the arm and the external world. These internal models are adaptive, learned with practice, and appear to be a fundamental part of voluntary motor control. However, very little is known about which neural structures are involved in formation of these internal models or how they learn to represent them. The aim here is to combine behavioral, neurophysiological and mathematical tools to infer how internal models are encoded in the cerebral cortex, by considering tasks in which the physical dynamics of reaching movements are altered. The working hypothesis is that the ability of subjects to learn and generalize motor skills is determined by how different kinematics parameters (e.g., direction, position) are encoded in the global tuning functions of cortical neurons, which in turn determines how error-dependent learning mechanisms adapt the internal models for task dynamics. This hypothesis will be tested in part by relating the observed tuning functions of motor cortical neurons to motor performance of subjects in a variety of tasks. To study the adaptation process itself, specific projects will ask how an error experienced in a given movement affects subsequent movements. These observations permit the definition of generalization functions that describe mathematically how the brain adapts the internal model in response to an error. The shape of this function predicts the tuning properties for movement kinematics of the elements that take part in representing the internal model. The generalization functions will be studied in the parameter spaces of arm position and velocity, and these inferred representations will be compared with the trial-to-trial response variability of motor cortex neurons. Further projects will extend learning from the procedural level of associating task dynamics with arm kinematics, to the cognitive level of linking dynamics to arbitrary cues such as the spatial location or color of visual stimuli.